We studied femtosecond spin dynamics in ${\mathrm{Ni}}_x{\mathrm{Pd}}_{1-x}$ magnetic thin films by optically pumping the system with infrared (1.55 eV) laser pulses and subsequently recording the reflectivity of extreme ultraviolet (XUV) pulses synchronized with the pump pulse train. XUV light in the energy range from 20 to 72 eV was produced by laser high-harmonic generation. The reflectivity of XUV radiation at characteristic resonant energies allowed separate detection of the spin dynamics in the elemental subsystems at the $M_{2,3}$ absorption edges of Ni (68.0 and 66.2 eV) and $N_{2,3}$ edges of Pd (55.7 and 50.9 eV). The measurements were performed in transversal magneto-optical Kerr effect geometry. In static measurements, we observed a magnetic signature of the Pd subsystem due to an induced magnetization. Calculated magneto-optical asymmetries based on density functional theory show close agreement with the measured results. Femtosecond spin dynamics measured at the Ni absorption edges indicates that increasing the Pd concentration, which causes a decrease in the Curie temperature $T_{\text{C}}$, results in a drop of the demagnetization time ${\tau }_{\text{M}}$, contrary to the ${\tau }_{\text{M}}\sim 1/T_{\text{C}}$ scaling expected for single-species materials. This observation is ascribed to the increase of the Pd-mediated spin-orbit coupling in the alloy.